Recent content by HappyN

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    Tossing a coin until it lands head up

    A coin with unknown probability p of landing head up when tossed, was tossed until it first landed head up. It happened on the 5th toss. Describe an appropriate statistical model for this experiment and write down the observed Likelihood function L(p). I assumed this was the same as...
  2. H

    How to show something is a subspace

    Do you mean the 7 axioms? like: v+w=w+v for all v,w € V (v+w)+z=v+(w+z) etc?
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    How to show something is a subspace

    How would you show that {(x,y,z) € R^3 :√11x - √13z=0} is a subspace of R^3? I know you have to make sure it fits the definition of a subspace, i.e prove u+v € W and alpha(v) € W but I am not sure how you would do this using √11x - √13z=0 ?
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    A function which is continuous on Z only

    I got f(x)={ x x € Q {-x otherwise not sure if that is right though?
  5. H

    A function which is continuous on Z only

    Thanks, I'm not quite sure what you mean by 'repeat it' though? If a function is only continuous at the origin surely it is not continuous on all Z?
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    How to find the basis for a set of vectors

    Homework Statement The question states: Consider the subset S of R^4 given by: S={(2,3,-1,7), (1,0,1,3), (0,3,-3,1), (12,15,-3,29)} i) Decide whether the vectors in S form a linearly independent set. ii) Let V be the vector subspace of R^4 spanned by the vectors of S, i.e: V=span{...
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    Continuous Functions Homework: Examples & Justification

    Homework Statement Find an example of a continuous function f:R->R with the following property. For every epsilon >0 there exists a delta >0 such that |f(x)-f(y)| <epsilon whenever x,y e R with |x-y|<delta. Now find an example of a continuous function f:R->R for which this property does nto...
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    Examples which satistfy f(x+y)=f(x) + f(y)

    Thanks HallsofIvy, I managed to make it work from your outline :) Wasn't sure about the Newton quotient though...
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    A function which is continuous on Z only

    I have spent ages on this final part of a question but don't seem to be going anywhere - any help would be greatly appreciated! Given a function f:R->R let X be the set of all points at which f is continuous. Find an example of a function defined on R which is continuous on Z only.
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    Examples which satistfy f(x+y)=f(x) + f(y)

    The question states: Give two different examples of f:R->R such that f is continuous and satisfies f(x+y)=f(x)+f(y) for every x,y e R. Find all continuous functions f:R->R having this property. Justify your answer with a proof. I came up with one example: f(x)=ax then...
  11. H

    Calculating E[x] for f(x)=e^-2|x| distribution in the reals (x e R)

    To calculate E[X] I did: ∫xf(x) dx (integral bounds between minus ∞ and ∞ - sorry don't know how to type it properly!) using integration by parts, i got: E[x]=[-x/2 e^-2|x|] + [1/4 e^-2|x|] (bounds evaluated between -∞ and ∞) =(-∞/2 e^-2|∞|) - (∞/2 e^-2|∞|) + (-1/4 e^-2|∞| + 1/4 e^-2|∞|)...
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    Calculating E[x] for f(x)=e^-2|x| distribution in the reals (x e R)

    do you mean my bounds are wrong? i'm not quite sure of what you mean by adjusting the integral for negative x?
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    Calculating E[x] for f(x)=e^-2|x| distribution in the reals (x e R)

    I want to calculate E[x] of the following continuous distribution having density: f(x)=e^-2|x| for x in the reals (x e R) I did the calculation with integral bounds infinity and minus infinity, are these the right bounds to use since we are only told x e R? I got 0 as the answer, can someone...
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    How can Taylor Series help us find a value of h for a specific error tolerance?

    how would you use Taylor Series to answer this: Find a value of h such that for |x|<h implies sin(x)=x-x^3/6 +x^5/120 + R where |R|< 10^-4?
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    How to show I_n + A is invertible

    Let A be an n x n matrix such that A^k=0_n,n (the n x n zero matrix) for some natural integer k. How would you show that I_n + A is invertible?
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